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Time Series Regression On Integrated Continuous-Time Processes With Heavy And Light Tails

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  • Fasen, Vicky

Abstract

The paper presents a cointegration model in continuous time, where the linear combinations of the integrated processes are modeled by a multivariate Ornstein–Uhlenbeck process. The integrated processes are defined as vector-valued Lévy processes with an additional noise term. Hence, if we observe the process at discrete time points, we obtain a multiple regression model. As an estimator for the regression parameter we use the least squares estimator. We show that it is a consistent estimator and derive its asymptotic behavior. The limit distribution is a ratio of functionals of Brownian motions and stable Lévy processes, whose characteristic triplets have an explicit analytic representation. In particular, we present the Wald and the t-ratio statistic and simulate asymptotic confidence intervals. For the proofs we derive some central limit theorems for multivariate Ornstein–Uhlenbeck processes.

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  • Fasen, Vicky, 2013. "Time Series Regression On Integrated Continuous-Time Processes With Heavy And Light Tails," Econometric Theory, Cambridge University Press, vol. 29(1), pages 28-67, February.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:01:p:28-67_00
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    Cited by:

    1. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    2. Sepideh Mosaferi & Mark S. Kaiser, 2021. "Nonparametric Cointegrating Regression Functions with Endogeneity and Semi-Long Memory," Papers 2111.00972, arXiv.org, revised Aug 2022.
    3. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.

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